Xiaohong Chen, Yuan Liao, Weichen Wang
arXiv 31 Dec 2022 · Statistics — Machine Learning
arXiv:2301.00092 · PDF · DOI · OpenAlex · Extracted main text
General nonlinear sieve learnings are classes of nonlinear sieves that can approximate nonlinear functions of high dimensional variables much more flexibly than various linear sieves (or series). This paper considers general nonlinear sieve quasi-likelihood ratio (GN-QLR) based inference on expectation functionals of time series data, where the functionals of interest are based on some nonparametric function that satisfy conditional moment restrictions and are learned using multilayer neural networks. While the asymptotic normality of the estimated functionals depends on some unknown Riesz representer of the functional space, we show that the optimally weighted GN-QLR statistic is asymptotically Chi-square distributed, regardless whether the expectation functional is regular (root-$n$ estimable) or not. This holds when the data are weakly dependent beta-mixing condition. We apply our method to the off-policy evaluation in reinforcement learning, by formulating the Bellman equation into the conditional moment restriction framework, so that we can make inference about the state-specific value functional using the proposed GN-QLR method with time series data. In addition, estimating the averaged partial means and averaged partial derivatives of nonparametric instrumental variables and quantile IV models are also presented as leading examples. Finally, a Monte Carlo study shows the finite sample performance of the procedure
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Shen, X (1997) On methods of sieves and penalization | 0.843 | 3 | 3 | 100% |
| 2 | Chen, X. and Pouzo, D (2015) Sieve wald and qlr inferences on semi/nonparametric conditional moment models self | 0.737 | 3 | 2 | 100% |
| 3 | Chen, X. and Qi, Z (2022) On well-posedness and minimax optimal rates of nonparametric q-function estimation in off-policy evaluation self | 0.737 | 3 | 2 | 100% |
| 4 | Ai, C. and Chen, X (2012) The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions self | 0.644 | 2 | 2 | 100% |
| 5 | Chernozhukov, V., Newey, W. K. and Singh, R (2018) Automatic debiased machine learning of causal and structural effects | 0.644 | 2 | 2 | 100% |
| 6 | Duan, Y., Wang, M. and Wainwright, M. J (2021) Optimal policy evaluation using kernel-based temporal difference methods | 0.644 | 2 | 2 | 100% |
| 7 | Fan, J., Wang, Z., Xie, Y. and Yang, Z (2020) A theoretical analysis of deep Q-learning | 0.644 | 2 | 2 | 100% |
| 8 | Farahmand, A.-m., Ghavamzadeh, M., Szepesvári, C. and Mannor, S (2016) Regularized policy iteration with nonparametric function spaces | 0.644 | 2 | 2 | 100% |
| 9 | Geist, M., Scherrer, B. and Pietquin, O (2019) A theory of regularized markov decision processes | 0.644 | 2 | 2 | 100% |
| 10 | Long, J., Han, J. and E, W (2021) An $l^2$ analysis of reinforcement learning in high dimensions with kernel and neural network approximation | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 46 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | High Dimensional Time Series Regression Models: Applications to Statistical Learning Methods | 0.405 | 1 | 1 |
| 2 | Conditional nonparametric variable screening by neural factor regression | 0.000 | 2 | 1 |